Analysis of high-order finite elements for convected wave propagation

作者：Beriot Hadrien^*; Gabard Gwenael; Perrey Debain Emmanuel

来源：International Journal for Numerical Methods in Engineering, 2013, 96(11): 665-688.

DOI：10.1002/nme.4559

• finite element method
• dispersion analysis
• high-order elements
• p-FEM
• convected propagation

In this paper, we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as bubble' shape functions. A series of simple test cases are also presented to support the results of the dispersion analysis. The main conclusion is that the properties of p-FEM that make its strength for standard acoustics (e.g., exponential p-convergence, low dispersion error) remain present for flow acoustics as well. However, the flow has a noticeable effect on the accuracy of the numerical solution, even when the change in wavelength due to the mean flow is accounted for, and an approximation of the dispersion error is proposed to describe the influence of the mean flow. Also discussed is the so-called aliasing effect, which can reduce the accuracy of the solution in the case of downstream propagation. This can be avoided by an appropriate choice of mesh resolution.

• 出版日期2013-12-14